Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-3x+9y &= -3 \\ -2x-6y &= 8\end{align*}$
Solution: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-2x = 6y+8$ Divide both sides by $-2$ to isolate $x$ $x = {-3y - 4}$ Substitute this expression for $x$ in the first equation. $-3({-3y - 4}) + 9y = -3$ $9y + 12 + 9y = -3$ Simplify by combining terms, then solve for $y$ $18y + 12 = -3$ $18y = -15$ $y = -\dfrac{5}{6}$ Substitute $-\dfrac{5}{6}$ for $y$ in the top equation. $-3x+9( -\dfrac{5}{6}) = -3$ $-3x-\dfrac{15}{2} = -3$ $-3x = \dfrac{9}{2}$ $x = -\dfrac{3}{2}$ The solution is $\enspace x = -\dfrac{3}{2}, \enspace y = -\dfrac{5}{6}$.